Mechanics of Materials - Civil Engineering Problems.pdf14 January 2011 2 3 Torsion Problems For the...

14 January 2011

1

Mechanics of Materials CIVL 3322 / MECH 3322

Torsion Problems

Homework

¢ P 6.17 ¢ P 6.18 ¢ P 6.20

Torsion Problems 2

14 January 2011

2

Torsion Problems 3

For the material properties shown in Figure 1, what is the Modulus of Elasticity of the material?

260 GPa 110 GPa 800 GPa 358 GPa

Torsion Problems 4

For the material properties shown in Figure 1, what is the ultimate strength of the material?

210 MPa 290 MPa 320 MPa 380 MPa

14 January 2011

3

Torsion Problems 5

For the material properties shown in Figure 1, what is the yield strength of the material?

210 MPa 290 MPa 320 MPa 380 MPa

Torsion Problems 6

For the material properties shown in Figure 1, what is the fracture stress of the material?

210 MPa 290 MPa 320 MPa 380 MPa

14 January 2011

4

Torsion Problems 7

The rigid bar shown in Figure 2 is supported by the pin at A and the rod from B to D (1). The rod (1) has a cross sectional area of 500 mm2, an elastic modulus of E = 80 GPa, and a coefficient of thermal expansion of a= 22x10-6/C. Initially the bar ABC is in a horizontal position, then the temperature of the rod (1) is reduced by 40°C. What is the deflection of point C after the temperature is reduced if the load P is equal to 0?

When rod (1) is cooled, point B will

Torsion Problems 8

1.  Move Up 2.  Move Down 3.  Not Move 4.  Don’t Know

14 January 2011

5

The magnitude of the deflection of point C will be _____ than the magnitude of the deflection of point B when Rod (1) is cooled.

Torsion Problems 9

1.  Equal to 2.  Less than 3.  Greater than 4.  Don’t Know

Torsion Problems 10

The rigid bar shown in Figure 2 is supported by the pin at A and the rod from B to D (1). The rod (1) has a cross sectional area of 500 mm2, an elastic modulus of E = 80 GPa, and a coefficient of thermal expansion of a= 22x10-6/C. Initially the bar ABC is in a horizontal position, then the temperature of the rod (1) is reduced by 40°C. What is the deflection of point C after the temperature is reduced if the load P is equal to 0?

( )( ) ( )( )33.3 10 3.05.66

1.75B AC

CAB

m mLmm

L mδ

δ−− ×

= = = −

14 January 2011

6

Torsion Problems 11

The rigid bar shown in Figure 2 is supported by the pin at A and the rod from B to D (1). The rod (1) has a cross sectional area of 500 mm2, an elastic modulus of E = 80 GPa, and a coefficient of thermal expansion of a= 22x10-6/C. Initially the bar ABC is in a horizontal position, then the temperature of the rod (1) is reduced by 40°C. What magnitude would P have to be to return the rod to a horizontal orientation after the temperature is reduced?

To solve for P, you would most likely

Torsion Problems 12

1.  Sum forces in the y-direction 2.  Sum forces in the x-direction 3.  Sum moments about A 4.  Don’t Know

14 January 2011

7

To find the force in rod (1) directly, you would most use

Torsion Problems 13

1.  The deflection at C 2.  The deflection at A 3.  The deflection at B 4.  Don’t Know

Torsion Problems 14

The rigid bar shown in Figure 2 is supported by the pin at A and the rod from B to D (1). The rod (1) has a cross sectional area of 500 mm2, an elastic modulus of E = 80 GPa, and a coefficient of thermal expansion of a= 22x10-6/C. Initially the bar ABC is in a horizontal position, then the temperature of the rod (1) is reduced by 40°C. What magnitude would P have to be to return the rod to a horizontal orientation after the temperature is reduced?

( )( )( )

( )( )( )

1 35.2 1.7520.53

3.0AB

AC

F L kN mP kN

L m− −

= = =

14 January 2011

8

Torsion Problems 15

Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. ESTEEL = 200 GPa and EBRASS = 105 GPa. What is the magnitude of the support reaction at point A?  

Torsion Problems 16

Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. ESTEEL = 200 GPa and EBRASS = 105 GPa.

What is the magnitude of the support reaction at point E?

3760 40 60 40 62 .19.81E AR kN kN R kN kNkN kN= + − = + − =

14 January 2011

9

Torsion Problems 17

Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. ESTEEL = 200 GPa and EBRASS = 105 GPa.

What is the deflection of point C?

Torsion Problems 18

Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. ESTEEL = 200 GPa and EBRASS = 105 GPa.

What is the stress in the Steel rod in the section between points A and B?

2

62.81 49.981257

ABAB

Steel

F kN MPaA mm

σ = = =

14 January 2011

10

Torsion Problems 19

Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. ESTEEL = 200 GPa and EBRASS = 105 GPa.

What is the stress in the Brass rod in the section between points D and E?

2

37.19 52.62706.86

DEDE

Brass

F kN MPaA mm

σ = − = − = −

Torsion Problems 20

The rigid bar AD is supported by two steel wires of 1/16 -in. diameter (E = 29x106 psi) and a pin at D. The bar is horizontal before the load P is applied. The load P has a magnitude of 120-lb. After P is applied What is the tension in the wire from A to E?

14 January 2011

11

The relationship between the deflections at A and C is

Torsion Problems 21

1.  EA>FC

2.  EA=FC

3.  EA>FC

4.  Don’t Know

The relationship between the deflections at A and C is

Torsion Problems 22

1.  EA>FC

2.  EA=FC

3.  EA>FC

4.  Don’t Know

14 January 2011

12

Torsion Problems 23

The rigid bar AD is supported by two steel wires of 1/16 -in. diameter (E = 29x106 psi) and a pin at D. The bar is horizontal before the load P is applied. The load P has a magnitude of 120-lb. After P is applied What is the tension in the wire from A to E?

( )( ) ( )( ) ( )

58

516 120 24 88

66.21

CF AE

AE AE

AE

F F

in lb in F in F

F lb

=

⎛ ⎞= + ⎜ ⎟⎝ ⎠=

Torsion Problems 24

The rigid bar AD is supported by two steel wires of 1/16 -in. diameter (E = 29x106 psi) and a pin at D. The bar is horizontal before the load P is applied. The load P has a magnitude of 120-lb. After P is applied What is the tension in the wire from C to F?

66.215 5 66.21 41.388 8

AE

CF AE

F lb

F F lb lb

=

= = =

14 January 2011

13

Torsion Problems 25

The rigid bar AD is supported by two steel wires of 1/16 -in. diameter (E = 29x106 psi) and a pin at D. The bar is horizontal before the load P is applied. The load P has a magnitude of 120-lb. After P is applied What is the strain in the wire from A to E?

( )( )( )( )3 2 6

66.21 150.11

3.07 10 29 10

0.11 0.0067 /15

AE AEAE

AEAE

AE

lb inF L inAE in psi

in in inL in

δ

δε

−= = =

× ×

= = =

Torsion Problems 26

The rigid bar AD is supported by two steel wires of 1/16 -in. diameter (E = 29x106 psi) and a pin at D. The bar is horizontal before the load P is applied. The load P has a magnitude of 120-lb. After P is applied What is the deflection of point B from the original unloaded horizontal position?

( ) ( )( )16

0.11 0.07324B AE

inBD in inAD in

δ δ= = =

14 January 2011

14

Problem 6.4

Torsion Problems 27

Problem 6.12

Torsion Problems 28

14 January 2011

15

Problem 6.16

Torsion Problems 29